Answer:
2.5 pi
Step-by-step explanation:
Comment
If you were trying to get the area of a whole circle, you would use
Area = pi r^2
You have to modify the formula to show that just part of the circle has an area that you are interested in.
The new formula is
Area = (theta/360) pi r^2
Givens
r = 30 cm
theta = 100
Solution
Area = (100 / 360) * pi * r^2 Substitute the givens into this formula
Area = (5 / 18) * pi * 3^2 Expand
Area = (5 / 18) * pi * 9 Cancel 9 into 18
Area = 5/2 * pi
Area = 2.5 * pi
Hello, I need help understanding the following question.
Answer:
option b, y = 3/4x - 11
Step-by-step explanation:
Parallel lines have the same slope,
slope = rise / run where the rise is 3 and the run is 4
slope = 3/4
The line is in a upwards trend making the slope positive making choice c and d incorrect
The line passes through (8, -5)
y = 3/4x + b, (x, y)
-5 = 3/4(8) + b
-5 = 6 + b
-5 - 6 = 6 - 6 + b
-5 - 6 = b
-11 = b
y = 3/4x - 11
Help me with this question please!!!
Question 1
We want to choose a white marble, then a black marble.
The probability of choosing a white marble is 9/(9+7+8)=9/24.The probability of choosing a black marble is 8/(9+7+8)=8/24.Multiplying these probabilities, we get (9/24)(8/24) = 1/8.
Question 2
For the guess to be less than 6, they have to choose 1, 2, 3, 4, or 5.Thus, the probability is 5/10 = 1/2.
Question 3
The probability of choosing a yellow marble is 7/(7+8+9)=7/24.The probability of choosing a green marble after is 9/(6+8+9)=9/23. [Note that the 7 yellow marbles is now 6 since we are assuming a yellow marble was drawn beforehand]Multiplying these probabilities, we get (7/24)(9/23) = 21/184.
A hole the size of a photograph is cut from a red piece
of paper to use in a picture frame.
3
What is the area of the piece of red paper after the hole
for the photograph has been cut?
O 17 square units
O 25 square units
O 39 square units
O 47 square units
Answer:
D)
Step-by-step explanation:
47 is the right answer! Have an cool day!
The area of the piece of red paper after the hole for the photograph has been cut is,
⇒ 47 square units.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Now, First, find the area of the two squares:
The photograph have vertices:
(-3, -2), (-2, 2), (2, 1), and (1, -3).
Since, The square is diagonally aligned, so we need to find the length between two points in order to find the area.
For (1, -3) and (2, 1).
There is a 1 unit length and a 4 unit height.
We can use the Pythagorean theorem to find the hypotenuse of the triangle, which is the length of the square's side:
1² + 4² = x²
1 + 16 = x²
x = √17
The side length for the square of the photograph is the square root of 17,
so the area of the photograph is 17 units²
Now, The red paper has side lengths of 8. The distance between (-4, 4) and (4, 4) is 8 units wide, so we do not need to use the Pythagorean theorem.
Now , we know the area of the red paper and photograph, you can subtract the area to find the red paper with the hole:
64 - 17 = 47 square units.
Thus, The area of the piece of red paper after the hole for the photograph has been cut is,
⇒ 47 square units.
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Explain the order in which to simplify the following and then simplify it.
Answer:
16 x^14 / y^16
Step-by-step explanation:
Remember ' PEDMAS '
Parentheses
Exponents
Division
Multiplication
Addition
Subtraction
so do the stuff inside the parentheses to get
y^8 ^-2
4x^7
Now do the exponents ( the -2 one)
y^-16
4^-2 x^-14 then simplify
16 x^14 / y^16
The first term of a sequence is 5.
The term-to-term rule is 'add 8'. What is the 10th term of the sequence?
Answer:
[tex]\fbox {77}[/tex]
Step-by-step explanation:
Given
⇒ a = 5
⇒ d = + 8
Solving :
⇒ a₁₀ = a + 9d
⇒ a₁₀ = 5 + 9(8)
⇒ a₁₀ = 5 + 72
⇒ a₁₀ = 77
find the perimeter of the triangle
Answer:
x²+14x+11
Step-by-step explanation:
Find the perimeter of the triangle.
The perimeter is:
add them
-x²+9x
2x²+6
5x+5
x²+14x+11
quizlet
−3x(4x² − 81) (x² + 64) = 0
Answer: [tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]-3x(4x^2-81)(x^2+64)=0\\[/tex]
multiply the terms together
[tex]-12x^5-525x^3+15552x=0[/tex]
factor left side of the equation
[tex]3x(-x^2-64)(2x+9)(2x-9)=0[/tex]
set factors equal to 0
[tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]
yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
The inverse of 3 and _ 5
Answer:
Sorry I don't know the answer
Consider the matrix [tex]A_{4x4}, det(A) = -2[/tex]
Show that the following is true or false:
[tex]det(adj(2A^{-1}) =-2^{9}[/tex]
We found a counterexample, so the statement is false.
Is the statement true?
Let's use the matrix:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]
If we multiply it by 2, we get:
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]
The adjoint of that is the original matrix, actually:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
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ratio of pi?
3. whats an estimation that's fraction form?
Answer:
22/7
Step-by-step explanation:
22/7 is not very close to pi, but it is sometimes used as an estimation for pi
Answer:
22/7 is estimation
Evaluate iint S sqrt 1+x^ 2 +y^ 2 dS where S is the helicoid: r(u, v) = u * cos (v) * i + u * sin (v) * j + vk with 0 <= u <= 1, 0 <= v <= 2pi
Given the parameterization
[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]
take the normal vector to be
[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]
(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)
Compute the magnitude of the normal vector.
[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]
so that the area element reduces to
[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]
Evaluate the integrand at [tex]\vec r[/tex] to get
[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]
The surface integral reduces to
[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]
How would you multiply 4x 2
—
3
( 4 x 2 by 3 (fractions))
Answer:
8/3
Step-by-step explanation:
4 x 2 = 8, so (4 × 2)/2 = 8/3.
Determine the equation of a line passing through the point (2,-6), with a slope of m=-1
Answer:
sub(2，-6)into y=mx+C
-6=-1(2)+C
C=-4
equation=y=-x-4
Answer:
y = -x - 4
Step-by-step explanation:
Given:
a line with a slope of -1, passing through the point (2,-6)
Point-Slope Form: y - y₁ = m(x - x₁)
where:
(x₁, y₁) is the given point
m is the slope
Substitute the given values into the formula:
⇒ y - y₁ = m(x - x₁)
⇒ y - (-6) = -1(x - 2)
⇒ y + 6 = -1(x - 2) [distribute -1 through the parentheses]
⇒ y + 6 = -x + 2 [subtract 6 from both sides]
⇒ y + 6 - 6 = -x + 2 - 6
⇒ y = -x - 4
Check your work:
⇒ y = -x - 4 [substitute 2 for x, and -6 for y]
⇒ -6 = -2 - 4 [simplify]
⇒ -6 = -6 ✔
Therefore, the equation of the line is: y = -x - 4
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Given: ∠E and ∠F are supplementary and ∠F and ∠G are supplementary.
Prove: ∠E≅∠G
1) ∠E and ∠F are supplementary and ∠F and ∠G are supplementary (given)
2) m∠E+m∠F=180 degrees, m∠F+m∠G=180 degrees (supplementary angles have measures that add to 180 degrees)
3) m∠E=m∠G (subtraction property of equality)
4) ∠E≅∠G (angles with equal measure are congruent)
Derek works 43 hours at a rate of pay of $15 per hour. He receives double pay over 40 hours. What is his gross pay?
The Gross pay which Derek gets is 690 dollars.
What is Gross Pay?Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages. The amount remaining after all withholdings are accounted for is net pay or take-home pay.
Here, Total hours worked by Derek = 43 hours
Rate of pay = $15 per hour
Rate of pay beyond 40 hours = $30 per hour
Now,
Rate of pay for the first 40 hours = 40 X 15 = $ 600
Since the pay rate doubles after 40 hours,
Rate of pay for the remaining 3 hours = 3 X 30 = $ 90
Gross Pay = 600 + 90 = $ 690
Thus, the Gross pay which Derek gets is 690 dollars.
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8) 3/
of the magazines sold at a newsagents were wedding magazines.
What is this as a percentage?
44
Answer:
0.0085× 100= 0.85℅
Step-by-step explanation:
okay so you want 3/8 from 44 as percentage but how can you put the 3/8 on top of the 44 to multilply it by 100 to get the percentage, ofcourse we will have to change the 3/8 into a whole number. To do that we are going to do the following.
= 3 ÷ 8 = 0.375, so here you got a number that you can put on the 44.
Now to get the percentage we are going to do this:
0.375/44 × 100
= 0.0085 × 100 ( I solved the 0.375/44 as you know that division always comes first in maths)
= 0.85℅ ( I solved the 0.0085 × 100)
°•°•° I hope this helped sorry for taking long °•°•° May I get brainliest if you liked my ans im trying to lvl up ty and its okay if you don't want to
The base of a triangle is 5 cm greater than the
height. The area is 33 cm². Find the height and
the length of the base.
Answer:
height= 13.2 cm
Step-by-step explanation:
h = 2 × A/b
h = 2 × 33 /5
= 13.2
If an investor invests $24,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple
interest, and the investor earns $700 annual interest, how much was invested in each account?
Round your answers to the nearest dollar.
2% bond: $
4% bond: $
Answers:
2% bond: $11000
4% bond: $13000
========================================================
Explanation:
x = amount invested in the 4% bond
y = amount invested in the 2% bond
Amounts are in dollars
The two amounts add to $24,000 so
x+y = 24000
y = -x+24000 is one equation to set up
0.04x = interest earned from the 4% bond
0.02y = interest earned from the 2% bond
0.04x+0.02y = total interest earned = $700
0.04x+0.02y = 700 is another equation to set up
------------
The system of equations is
[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]
Apply substitution. Solve for x.
0.04x+0.02y = 700
0.04x+0.02(-x+24000) = 700
0.04x-0.02x+480 = 700
0.02x= 700-480
0.02x= 220
x= 220/(0.02)
x = 11000
Use this to find y
y = -x+24000
y = -11000+24000
y = 13000
Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase. Which store offered the better discount, and how much is the difference?
The better option will be at DiscountsRUs 40% off on any purchase.
What is the discount?The amount of money which is reduced on any product below its actual selling price is called the discount.
here we have two offers from the two stores Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase.
For a Dominic, the discount is fixed for any purchase that is if you purchase a $50 product or a $1000 product you will be getting only a $15 discount.
Now for the second store, the discount is given as 40% so if you purchase $50 your discount will be $20. If you purchase $1000 so 40% discount will be $400.
Therefore better option will be at DiscountsRUs 40% off on any purchase.
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A wagon is being pulled by a handle making a 40° angle with a force of 35 pounds. What amount of force is moving the wagon along level ground? Round to the nearest tenth.
The amount of force is moving the wagon along ground level will be 26.8 pound
A force in physics is an effect that has the power to alter an object's motion. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction.
Given a wagon is being pulled by a handle making a 40° angle with a force of 35 pounds
We have to find amount of force is moving the wagon along level ground
The angle with force is given 40 degree
So the formula to find amount of force is moving the wagon along level ground will be as follow:
Fₓ = F cosθ
Fₓ = 35 * cos40
Fₓ = 26.8 pound
Hence amount of force is moving the wagon along ground level will be 26.8 pound
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10 times the sum of certain numbers x and y
This can be represented by [tex]\boxed{10(x+y)}[/tex]
if a tap leaks at the rate of 1 L per half minute, how many litres are Lost after 10 minutes?
Answer:
The answer is 20 L
Step-by-step explanation:
if 1/2 minutes = 1 L
10 minutes = 20 L
Answer:
20 liters
Step-by-step explanation:
when working with math problems about the rate that something is happening, it is typically helpful to find the unit rate.
In this case, the unit rate will be how many liters are lost in 1 minute (per unit essentially means per "1" )
we know that 1 liter is lost in 1/2 minute
1/2 minute = 1 liter
×2 ×2 {multiply both sides by 2 to find "1 minute"}
1 minute = 2 liters
So, for every 1 minute, we lose 2 liters
if we have 10 minutes, we can multiply both sides by 10:
1 minute = 2 liters
×10 ×10
10 minutes = 20 liters
So, after 10 minutes, 20 liters are lost
hope this helps!!
Help me with this please and thank you!! :)
Answer:
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the set of elements in both A and C, which is [tex]\{20, 24, 28\}[/tex].[tex]B^{C}[/tex] denotes the complement of set B, which is the set of all elements that are in the universal set that are not in set B. In this case, this set is [tex]\{3, 4, 5, 6, 8, 11, 13, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28\}[/tex]What’s the slope of this graph? Can y’all guys help please ! Thank y’all
Answer:
3
Step-by-step explanation:
we can think of the slope of a graph as [tex]\frac{rise}{run}[/tex]
the "rise" is the difference in y-values between two points (the change in y)
the "run" is the difference in x-values between two points (the change in x)
when we divide these (rise/run), we find the slope
you can choose any two well-defined points (with clear x and y values), here are the two we will be using:
(remember, points are written as (x, y) )
(0 , 2)
(-1 , -1)
for the "rise", we have risen 3 (difference between 2 and -1 = 3 [2- -1 = 3] )
for the "run" we have ran 1 (difference between 0 and -1 = 1) (0 - - 1 = 1)
so, the slope for this graph is: 3/1 ; which simplifies to 3
So, the slope of our graph is 3
--------------------------------------------------------------
technical layout:
[tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex] (note: slope is called "m" in the format of y=mx + b)
[tex]y_{1}[/tex] means one y-value, [tex]y_{2}[/tex] means other y-value
[tex]x_{1}[/tex] means one y-value, [tex]x_{2}[/tex] means other x-value
{note: it is important to keep the y1 and x1 from the same point, and the y2 and x2 from a shared point}
our equation in this layout:
[tex]m=\frac{2 -(-1)}{0-(-1)}[/tex] = [tex]m=\frac{3}{1}[/tex]
m = 3
One leg of a 90-45-45 triangle is 5. What are the sides of the hypotenuse and the other leg?
Answer:
5√2, 5
Step-by-step explanation:
in a 90 45 45 triangle, each leg is the same legnth
the hypotenuse of a 90 45 45 triangle is x√2
x being the measure of the leg
Find the radius of a circle with area 345 square centimetres
For 35 points need asap in 10 MINS!!!! :)
5.9
Step-by-step explanation:
345√ is 18.6=3.14*r2 cuz formula
Is πr2
What is the slope intercept of the line below
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option D, y = 2x - 3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The graph}[/tex]
Find: [tex]\textsf{The equation in slope intercept form}[/tex]
Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept. All we need to do now is find a second point so we can determine the slope. The line crosses at (1, -1) so we will use that as the second point. Then we just plug all of the values into the slope intercept form.
Determine the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{-1 - (-3)}{1 - 0}[/tex][tex]m = \frac{-1 + 3}{1}[/tex][tex]m = \frac{2}{1}[/tex][tex]m = 2[/tex]Plug in the values
[tex]y = mx + b[/tex][tex]y = 2x - 3[/tex]Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.
Which of the following linear equations passes through points (-1,5) and (1,-5)?
Y=-5x
Y=5x+10
Y=-2x+3
Answer:
y = -5x
Step-by-step explanation:
gradient = delta y / delta x
gradient = -10 / 2
gradient = -5
y = mx + b
5 = -5(-1) + b
5 = 5 + b
b = 0
y = -5x
We can describe 3x- 2 as an expression. How can we describe the parts of the expression that the arrows point to? 3x- 2
Step-by-step explanation:
3x - 2 is formatted in the formula y = mx + c
To substitute for 3x - 2
y = 3x -2
What is the range of the function graphed below?
